Our LDT mfg give us all kinds of weight numbers such as a payload stickers/truck camper weight stickers/CCC numbers/GVWR FAWR/RAWR/GCWR/numbers in a brochure/etc/etc , you get the picture.
First off trucks don't carry weight in any legal sense by using the trucks GVWR.
Thats where the trucks GAWR/tire load rating come to play.
GM gives your 3500 SRW a 7050 RAWR which on a crew cab long bed will carry just about all of a TC's weight.
Now this is where you need your trucks actual front and rear axle weights. Forget a gross weight unless your truck is required to be registered at a gross.
I'll use some numbers here from other one ton SRW owners rear axle weights but many may weigh in the 3000-3200 lb range which leaves you with a 3800-4000 lbs for a payload. Your actual weights will vary but you get the picture.
Lots get said about LDT and their TC weight numbers. IMO it and some of the other weight numbers are more a CYA liability issue from the truck makers.